如图,抛物线
恰好经过
,
,与
轴交于另一点
,
为抛物线的顶点,点
是抛物线上一动点.
(1)求抛物线的表达式;
(2)当
时,求点
的坐标;
(3)点
是抛物线对称轴上一动点,是否存在以点
,
,
为顶点的三角形是等腰三角形?若存在,请直接写出
点坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e59da5115d0dafea24822245f92c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ef03f452410ab19c6246567c427178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c052d7af2f98d95bac8725b608fba0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/26/ef3aa273-6f61-47f8-be09-ee5ebd58b6aa.png?resizew=405)
(1)求抛物线的表达式;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d193887b91e77feb497f54c7742561ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
更新时间:2023-06-25 11:02:07
|
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【推荐1】如图,在平面直角坐标系中,一次函数y=kx+b的图象经过点A(0,﹣4)、B(2,0),交反比例函数y
(x>0)的图象于点C,点P在反比例函数的图象上,横坐标为n(0<n<3),
轴交直线AB于点Q,D是y轴上任意一点,连接PD、QD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/28/af5cc469-4952-479a-891b-79f463f3c097.png?resizew=184)
(1)求一次函数的表达式和C点坐标;
(2)求△DPQ面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69743e0712fa8787a3fbd42d0030c367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f27083267432a9352fb6677a07d461.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/28/af5cc469-4952-479a-891b-79f463f3c097.png?resizew=184)
(1)求一次函数的表达式和C点坐标;
(2)求△DPQ面积的最大值.
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【推荐2】疫情之下,中国充分发挥了集中力量办大事的制度优势,一方需要,八方支援.某防疫部门需要从A,B仓库向防疫点甲、乙两地分别运送
和
的防疫物资.已知A仓库存有
,B仓库存有
.从A,B两仓库运送到甲、乙两防疫点每吨的运费如下表:
(1)设从A仓库运送到甲防疫点的物资为
,求运送的总运费y(元)与
之间的函数解析式(也称函数关系式),并直接写出x的取值范围;
(2)请你设计出运费最低的运送方案,并求出最低运费.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1247810da7a9577bca230b8f12769326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46310681330e94e1a41f42333149a24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7641b9c5f06e3243d3f6bc5bae49c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01af3e772e354c1afcf2ba48b48c5936.png)
目的地 | 运费/(元/t) | |
A仓库 | B仓库 | |
甲防疫点 | 80 | 100 |
乙防疫点 | 60 | 40 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b114daafc3821d2ff021a912107de43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf0fce63dcd10861e7103d454443284.png)
(2)请你设计出运费最低的运送方案,并求出最低运费.
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适中
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名校
【推荐1】已知抛物线G:
与x轴交于点A,B(点A在点B的左侧),与y轴交于点C,点
为y轴上一动点,过点P作y轴的垂线交抛物线G于点M、N(M与N不重合).
(1)当
时,若
,求抛物线G的纵坐标在
时的取值范围;
(2)对于
的每一个确定的值,
有最小值m,若
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cdeab138c71dca786f36d1adde50ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f99ed70aeaecb5b2a68329ef2a69e76.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b049239999ee72964179868ed906db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6288f5c321391185797e3d6dc56b102.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70444e3a66d1068038c5b5a77c7954aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561800aa679a45da4dbe0e323de1fd59.png)
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名校
【推荐2】已知
是x的二次函数.
(1)当m取何值时,该二次函数的图象开口向下?
(2)在(1)的条件下
①当
时,求y的取值范围:
②当
时,求x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b956b2257cb6c82b601d9f5c229f3be.png)
(1)当m取何值时,该二次函数的图象开口向下?
(2)在(1)的条件下
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e28073a33bb987c70262c9a7e4fcec07.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea34b472e3a9fbd1fd256e23c909ea48.png)
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解答题-证明题
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适中
(0.65)
【推荐1】如图,四边形
内接于
,
平分
,交
于点
.
(1)如图1,求证:
.
(2)如图2,若
经过圆心
,且
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/23/678613f6-265d-46a8-bc79-6ac0745a1424.png?resizew=299)
(1)如图1,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4235c082f9505064230624268143ea4b.png)
(2)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
解答题-问答题
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适中
(0.65)
【推荐2】如图1,平面直角坐标系中,一次函数
的图像分别交
轴、
轴于点
,一次函数
的图像经过点
,并与
轴交于点
,点
是直线
上的一个动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/6cb2b44e-3508-4ef1-92e8-b4ca261b4639.png?resizew=388)
(1)
___________,
___________;
(2)如图2,当点
在第一象限时,过点
作
轴的垂线,垂足为点
,交直线
于点
.若
,求点
的坐标;
(3)是否存在点
,使以
为顶点的三角形是等腰三角形?若存在,请直接写出点
的横坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6dfd3d55a8807342b3fe7eb939f54cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/6cb2b44e-3508-4ef1-92e8-b4ca261b4639.png?resizew=388)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
(2)如图2,当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81c810f1ffd122e63cc04c44ef785153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(3)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb452339f63edb5369b899addce5b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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【推荐1】如图,在▱ABCD中,∠ACB=45°,AE⊥BC于点E,过点C作CF⊥AB于点F,交AE于点M.点N在边BC上,且AM=CN,连结DN.
(1)若AB=
,AC=4,求BC的长;
(2)求证:AD+AM=
DN.
(1)若AB=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4056761b8f826eeb6ad8c9a151d3c9c.png)
(2)求证:AD+AM=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2020/2/26/2407154167824384/2407435595104256/STEM/7856c07d3f3c47ac964fd7e9f8900ee7.png?resizew=188)
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【推荐2】如图,已知在平面直角坐标系
中,
,
,
,将
沿直线OB折叠,点A落在点D处,OD交BC边于点E,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/4/85b59798-59ec-47cb-8d34-f9b46cc48b35.png?resizew=200)
(1)求证:四边形OABC为矩形;
(2)求直线OD的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95e84f5c91c910aaafc5e74dbfbdf59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6419152065edb8cabf887b65adb4a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5558ffa6dc28d437c0467c7f361d444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/4/85b59798-59ec-47cb-8d34-f9b46cc48b35.png?resizew=200)
(1)求证:四边形OABC为矩形;
(2)求直线OD的解析式.
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